fmetric {mmpp}

Compute Filter-based Metrics in a Functional Space Between Marked Point Processes

Description

The most commonly used and intensively studied metrics for spike trains, which is based on the continuation of event sequence to a real valued continuous function using a smoother function.

Usage

fmetric(S1, S2, measure = "sim", h = "laplacian", tau = 1, M = NULL,
  abs.tol = .Machine$double.eps^0.25)

Arguments

S1

marked point process data.

S2

marked point process data.

measure

"sim" for similarity and "dist" for distance. Default "sim".

h

filtering function. Default "laplacian" offers significant computational advantage. A function can be specified here like h=function(x,tau) exp(-x^2/tau). The function should be square integrable and non-negative (not checked in the code).

tau

parameter for filtering function.

M

a precision matrix for filter of marks, i.e., exp( - r' M r) is used for filtering marks. It should be symmetric and positive semi-definite.

abs.tol

absolute tolerance for numerical integration.

Details

fmetric computes filter-based measure between MPP realizations. Discrete event timings are transformed into a continuous function by using a kernel smoother, and usual l2 inner product is adopted for defining the similarity between two point process realizations.

Value

Similarity or distance between two inputs (marked) point process S1 and S2.

Author(s)

Hideitsu Hino [e-mail], Ken Takano, Yuki Yoshikawa, and Noboru Murata

References

M. C. W. van Rossum. A Novel Spike Distance. Neural Computation, Vol. 13(4), pp. 751-763, 2001.

S. Schreiber, J.M. Fellous, P.H. Tiesinga, and T.J. Sejnowski. A new correlation-based measure of spike timing reliability, Neurocomputing, Vols. 52-54, pp. 925-931, 2003.

Examples

##The aftershock data of 26th July 2003 earthquake of M6.2 at the northern Miyagi-Ken Japan.
data(Miyagi20030626)
## time longitude latitude depth magnitude
## split events by 7-hour
sMiyagi <- splitMPP(Miyagi20030626,h=60*60*7,scaleMarks=TRUE)$S
N <- 10
tau <- 0.1
sMat <- matrix(0,N,N)
  cat("calculating fmetric with tau ",tau,"...")
 for(i in 1:(N)){
   cat(i," ")
   for(j in i:N){
     S1 <- sMiyagi[[i]]$time;S2 <- sMiyagi[[j]]$time
    sMat[i,j] <- fmetric(S1,S2,tau=tau,M=diag(1,4))
   }
 }
 sMat <- sMat+t(sMat)
 tmpd <- diag(sMat) <- diag(sMat)/2
 sMat <- sMat/sqrt(outer(tmpd,tmpd))
image(sMat)